Synthetic homo-poly-peptides provide good models for proteins, and their vibrational properties have been examined with well-established physical theories and methods, including inelastic neutron scattering and Raman spectroscopy. One aim of this work is to provide a complete understanding of the thermodynamics of biopolymers, for then one can predict conformations, helix-coil transitions, etc. An important thermodynamic quantity is the specific heat, which we have measured at low temperatures. We propose to measure the specific heats of synthetic homo-poly-peptides over the temperature range 100-400 K (negative 170 degrees, to positive 130 degrees C) using a recently improved differential scanning method, which has the advantages of being quick, cheap to perform and even available commercially. A great advantage of this method is that samples of less than a milligram can be measured; this is indispensable for many homo-poly-peptides, which are available only in small quantities. The information given by this method complements and overlaps that given by neutron scattering and Raman spectroscopy, and will stimulate further theoretical work. The disadvantage of this method is that it is only of one to two percent accuracy, but this disadvantage is far outweighed by the amount of information given, which is inaccessible to conventional (though more accurate) methods of measuring specific heats, since the latter require much larger samples. However, an accuracy of a few percent is certainly sufficient for most present theories. The proposed method can also detect polymer transition, can be used with tiny crystallites (which are often the largest crystals which can be grown), and can very easily be extended to other biopolymers, such as collagens, proteins, enzymes, and nucleic acids, and also to cellular components such as membranes. The results are of basic importance to studies of the thermodynamics and conformation of proteins and may well be of importance in understanding enzyme and membrane action.